Discounting for Public Projects

All our discussion so far has been concerned with discounting in private investment projects. To what extent should the conclusions be modified when evaluating investment projects under uncertainty? We now turn to this question.

The essential difference between a private and a public project is that the latter is to be evaluated on the basis of what is good for society as a whole. Western economists have traditionally assumed that redistribution will be taken care of by other public measures such as taxes, and that efficiency is the sole basis for project evaluation in general, and for the choice of a discount rate in particular. Even within that narrow frame of reference, there are two different views, which A. Sandmo summarizes well, about the proper discount rate:

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"One view, which has been advanced by Hirshieifer .... and supported by Diamond . ... is that differences in rates of return on capital in the private sector of the economy reflect differences in riskiness among alternative tines of investment, and that these differences are of normative significance for the allocation of capital in the public sector. Thus, when discounting costs and benefits of a particular type of public investment, the government should take as its discount rate the rate of return on capital in a private industry of simitar riskiness. Another view, which counts Samuelson . . . and Vickrey . . . among its supporters, is that because of the extremely large and diversified investment portfolio held by the public sector, the marginal return from public investment as a whole is practically risk-free and should be equated to the market rate on riskless bonds . . . Arrow and Lind come to the same conclusion. . . ” (Sandmo, p. 192).

Sandmo’s own analysis leads him to the first view that:

"the public sector’s discount rates should always contain a risk margin, and that this margin correspond to the one used in the private sector for investment in the same risk class. In the stock market economy this margin can be inferred directly from market data; in the unincorporated economy an averaging of individual risk margins is required". (Sandmo, pp. 207-08).

Let us now comment briefly on the Samuelson-Vickrey view that the marginal return from public investment is practically risk-free.

Arguing against Samuelson is seldom risk-free. I shall nonetheless indicate certain practical considerations that undermine the realism of Samuelson and Vickrey view.

We note first that Prest and Turvey (p. 171) take the definite stand that “ . . . there is no reason to argue that public investment projects are free from uncertainty ...” but they fail to elaborate. Secondly, we note that Samuelson-Vickrey argument is essentially statistical: the public sector’s investment is large and diversified, hence it is riskfree. This is another way of saying that the variance of the sum of the returns on public investment is less than the sum of variances of individual projects. (This is also one well-known argument for portfolio diversification.)

But for diversification to reduce risk, two conditions are required:

returns on different projects should be statistically independent and

the size of each project should be small relative to the total. Neither of these two conditions are often met in practice, especially in less developed economies. There, a single investment is often quite large relative to a given economy, (e.g. a steel mill or a major dam). Moreover, the same central administration selects and executes most of the country’s projects whose outcomes tend to be highly correlated as they are all subject to similar levels of (dis-) honesty and (in-) efficiency. This tends to make the returns on many projects highly correlated. This is particularly likely in marginal investment, which is crucial for decision and which is much smaller and less diversified than total public capital stock. Thus on purely empirical grounds, Samuelson-Vickrey argument is not, in our view, realistic. But in fairness to Vickrey and Samuelson we should add the following points:

Samuelson’s (1964) comments are quite circumspect. Nowhere he says (in pp. 93-6) that the government should apply a riskless interest rate to public projects. He even gives counter examples where a heavy “risk premium” is in order. He basically asserts that public investments have lower risk because of diversification.

Vickrey is quite emphatic in his view (pp. 88—92) that public investments are virtually risk-free. We have given answers to some but not all of his arguments.

The main conclusion of this section is that even from the narrow perspective of mere economic efficiency in capitalistic economy, one major view is that public investments should be discounted by a rate of return rather than by a riskless interest rate. There can thus be no question that in an Islamic economy which rejects interest and permits rates of return, discounting in public projects can and should be based on the latter rates, adjusted, when necessary, to achieve social optimality.